Course materials for 2020-11-2 AFEC at XTBG.
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Load pacakges.
## Illicium_macranthum Manglietia_insignis Michelia_floribunda
## Site1 1 0 0
## Site2 1 2 2
## Site3 1 0 0
## Site4 1 1 0
## Site5 1 0 0
## Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii
## Site1 0 0 0
## Site2 2 0 0
## Site3 0 0 2
## Site4 0 0 2
## Site5 0 1 1
## Actinodaphne_forrestii Machilus_yunnanensis
## Site1 0 0
## Site2 0 0
## Site3 2 2
## Site4 2 0
## Site5 0 0
| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait_long <- trait %>%
gather(trait, val, 2:9)
ggplot(trait_long, aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait %>%
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) %>%
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 %>%
gather(trait, val, 2:9) %>%
ggplot(., aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Skip
## Run 0 stress 0
## Run 1 stress 0
## ... Procrustes: rmse 0.05405595 max resid 0.07254661
## Run 2 stress 0.1302441
## Run 3 stress 0
## ... Procrustes: rmse 0.1292857 max resid 0.2054544
## Run 4 stress 0.0968098
## Run 5 stress 0.2297529
## Run 6 stress 0.09681173
## Run 7 stress 9.908224e-05
## ... Procrustes: rmse 0.12886 max resid 0.1986339
## Run 8 stress 0.09681171
## Run 9 stress 0.09681122
## Run 10 stress 0
## ... Procrustes: rmse 0.07643282 max resid 0.1299972
## Run 11 stress 0.1302441
## Run 12 stress 0.1302441
## Run 13 stress 0
## ... Procrustes: rmse 0.04906472 max resid 0.07985005
## Run 14 stress 0
## ... Procrustes: rmse 0.03960926 max resid 0.06420822
## Run 15 stress 0.1302441
## Run 16 stress 0.09681008
## Run 17 stress 1.636235e-05
## ... Procrustes: rmse 0.0363863 max resid 0.05159966
## Run 18 stress 0
## ... Procrustes: rmse 0.1359213 max resid 0.2236573
## Run 19 stress 0.09680968
## Run 20 stress 0
## ... Procrustes: rmse 0.05227704 max resid 0.07253967
## *** No convergence -- monoMDS stopping criteria:
## 9: stress < smin
## 7: stress ratio > sratmax
## 4: scale factor of the gradient < sfgrmin
We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sence.
ordiplot(res_mds, type = "n")
orditorp(res_mds,display="species",col="red",air=0.01)
orditorp(res_mds,display="sites",cex=1.25,air=0.01)cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
## Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii 0.0000000 0.18181818 0.18181818
## Melia_toosendan 0.1818182 0.00000000 0.09090909
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455
## Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.3636364 0.5454545
## Melia_toosendan 0.3636364 0.5454545
## Skimmia_arborescens 0.3636364 0.5454545
## Rhus_sylvestris 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.0000000
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
## [1] NA 1.568182 1.454545 1.606061 1.636364
The above vector shows MPD for each site.
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
## # A tibble: 8 x 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_f… 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_… 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macra… 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomso… 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunna… 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_ins… 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_flori… 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71
## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3
## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.4121097 -1.832581 0.48
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93
## Site5 14.713415 11.128090 12.759265 5.116104 0.2203436 -6.565585 1.52
## logSM
## Site1 0.3001046
## Site2 0.3114643
## Site3 -1.9909259
## Site4 2.2087792
## Site5 0.3257723
## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667
## logSM
## Site1 0.3001046
## Site2 0.0444949
## Site3 -0.2844180
## Site4 0.3681299
## Site5 0.1085908
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
Let’s see a subset of the trait matrix
## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037
Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])Now we can make a trait distance matirx.
Let’s see the first 5 species.
## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii 0.000000 3.799360 5.216902
## Actinodaphne_forrestii 3.799360 0.000000 2.415031
## Alnus_nepalensis 5.216902 2.415031 0.000000
## Anneslea_fragrans 3.175911 2.335392 3.225141
## Beilschmiedia_robusta 2.545269 2.565063 3.638183
## Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 3.175911 2.545269
## Actinodaphne_forrestii 2.335392 2.565063
## Alnus_nepalensis 3.225141 3.638183
## Anneslea_fragrans 0.000000 1.579930
## Beilschmiedia_robusta 1.579930 0.000000
## [1] NA 4.288349 3.530805 3.961248 3.438008
## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z
## Site1 1 NA NaN NA NA NA
## Site2 4 4.288349 3.695558 0.7849795 778 0.7551683
## Site3 4 3.530805 3.722477 0.7913265 444 -0.2422158
## Site4 4 3.961248 3.712059 0.7790724 655 0.3198542
## Site5 3 3.438008 3.734332 0.9701865 442 -0.3054296
## mpd.obs.p runs
## Site1 NA 999
## Site2 0.778 999
## Site3 0.444 999
## Site4 0.655 999
## Site5 0.442 999
We will make a functional dendrogram using clustring methods. We use UPGMA in this example.
## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.
## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974
## WD logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691 0.1665816
## Site3 0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.9701997
## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.0.2 (2020-06-22)
## os Ubuntu 20.04 LTS
## system x86_64, linux-gnu
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Etc/UTC
## date 2020-11-05
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date lib source
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## cellranger 1.1.0 2016-07-27 [1] RSPM (R 4.0.0)
## cli 2.0.2 2020-02-28 [1] RSPM (R 4.0.0)
## cluster 2.1.0 2019-06-19 [2] CRAN (R 4.0.2)
## colorspace 1.4-1 2019-03-18 [1] RSPM (R 4.0.0)
## crayon 1.3.4 2017-09-16 [1] RSPM (R 4.0.0)
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## yaml 2.2.1 2020-02-01 [1] RSPM (R 4.0.0)
##
## [1] /usr/local/lib/R/site-library
## [2] /usr/local/lib/R/library